Analytical treatment of a simple fluid adsorbed in a slit-pore

Abstract

A model for a simple fluid confined to a slit-pore (fluid sandwiched between two plane-parallel substrates with infinitesimally smooth surfaces) is presented. The analysis is based on thermodynamic perturbation theory, in which the free energy is split into a zero-order (unperturbed) contribution from a hard-sphere fluid reference system and a correction accounting for both fluid-fluid and fluid-substrate attractions. The correction is evaluated in the mean-field approximation and the (unperturbed) local density is assumed uniform in order to obtain a closed expression for the correction. The resulting equation of state has the same temperature and density dependence as the van der Waals equation of state for the bulk fluid, although it differs from the latter in that the a parameter (ap) is a function of the separation sz of the substrate surfaces. The inequality ap(sz)⩽ab holds, from which it follows that the critical temperature of the pore fluid is lower than that of the bulk fluid. For mesoscopic pores, the lowering is in semi-quantitative agreement with experiment. The excess coverage Γ is calculated for bulk isochoric paths T→T0b, where T0b is the bulk liquid-gas coexistence temperature for a given isochore. If the fluid-substrate attraction is great enough, Γ vs T may exhibit a discontinuity reflecting pore condensation. The model predicts pore condensation over a density range comparable with the experimental one.